In a bowl, combine Greek yogurt, olive oil, lemon juice, grated garlic, chopped dill, and salt. Whisk until smooth and creamy; set aside to let the flavors meld.

Fill a saucepan with water and add the distilled white vinegar, bringing it to a gentle simmer. Crack the eggs into separate ramekins, then gently slide them into the simmering water. Poach for about 3 minutes until the whites are set and yolks remain nice and runny.

Carefully use a slotted spoon to transfer the poached eggs to a paper towel-lined plate to absorb any excess water.

In a small pan over medium heat, melt the unsalted butter. Once melted, stir in the Aleppo pepper and let it cook for about 1 minute, until fragrant and slightly bubbly.

Spread the herbed yogurt evenly on plates; place two poached eggs atop each serving. Drizzle the peppery butter sauce generously over the eggs and garnish with extra herbs and a sprinkle of flaky salt. Serve warm with pita or crusty bread for scooping.